As per other answers, slug is stored in the post_name
property. While it could be accessed directly, I prefer the (underused) get_post_field()
function for accessaccessing post properties which have no proper API for them.
It requires post provided explicitly and doesn't default to the current one, so in full for the current post it would be:
$slug = get_post_field( 'post_name', get_post() );